Autoencoder

Deep learning

Combinatorics

Physics

Matrix completion

Mathematics

Domain (mathematical analysis)

Wireless

Politics

Algorithm

Image (mathematics)

Matrix (chemical analysis)

Gaussian

Rank (graph theory)

Mathematical analysis

Interpolation (computer graphics)

Political science

Artificial intelligence

Throughput

Composite material

Hankel matrix

Aloha

Materials science

Representation (politics)

Computer science

Quantum mechanics

Telecommunications

Convolutional neural network

IEEE Transactions on Medical Imaging

The annihilating filter-based low-rank Hankel matrix approach (ALOHA) is one of the state-of-the-art compressed sensing approaches that directly interpolates the missing k-space data using low-rank Hankel matrix completion. The success of ALOHA is due to the concise signal representation in the k-space domain, thanks to the duality between structured low-rankness in the k-space domain and the image domain sparsity. Inspired by the recent mathematical discovery that links convolutional neural networks to Hankel matrix decomposition using data-driven framelet basis, here we propose a fully data-driven deep learning algorithm for k-space interpolation. Our network can be also easily applied to non-Cartesian k-space trajectories by simply adding an additional regridding layer. Extensive numerical experiments show that the proposed deep learning method consistently outperforms the existing image-domain deep learning approaches.

${k}$ -Space Deep Learning for Accelerated MRI